Burgers方程的控制理论:Agrachev-Sarychev方法
偏微分方程分析
2017-12-29 v1 最优化与控制
摘要
本文致力于描述 Agrachev 与 Sarychev 于 2005 年提出的研究 Navier-Stokes 方程某些控制问题的一般方法。以一维 Burgers 方程为例阐明主要思想。我们首先简要讨论 Cauchy 问题并建立解算子的连续性性质。接着转向近似能控性性质,证明其可由二维外力实现。最后我们研究一种更强的性质,即同时证明有限维泛函的近似能控性与精确能控性。
引用
@article{arxiv.1712.09807,
title = {Control theory for the Burgers equation: Agrachev-Sarychev approach},
author = {Armen Shirikyan},
journal= {arXiv preprint arXiv:1712.09807},
year = {2017}
}
备注
This paper is an extended version of the lectures on the control theory delivered at the University of Iasi (Romania) in 2010. It will be published in Pure and Applied Functional Analysis (2018, volume 3, number 2). A short version was published earlier in the proceedings of the conference Journ\'ees EDP (Evian, 4-8 June 2007)